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Scheduling and dimensioning of heterogeneous energy stores, with applications to future GB storage needs

Stan Zachary

TL;DR

The paper tackles the scheduling and dimensioning of heterogeneous energy stores required for future net-zero electricity systems, where high renewable variability necessitates large-scale, multi-technology storage. It develops a value-function based framework that yields near-optimal real-time policies, reducing the per-step problem to a simple linear program under non-anticipatory assumptions. Theoretical results show that greedy policies suffice and that non-anticipatory strategies (e.g., GG DDF, GRTEF) perform well, with cross-charging enabling cooperation among stores. An applied GB case demonstrates substantial potential cost savings from a well-chosen mix of storage technologies, highlighting practical pathways for dimensioning long-term storage without foresight, and suggesting broader applicability to other regions.

Abstract

Future ``net-zero'' electricity systems in which all or most generation is renewable may require very high volumes of storage, provided jointly by a number of heterogeneous technologies, in order to manage the associated variability in the generation-demand balance. We consider the problems of scheduling and dimensioning such storage. We develop a value-function based approach to optimal scheduling, and show that, to a good approximation, the problem to be solved at each successive point in time reduces to a linear programme with a particularly simple solution. We show that approximately optimal scheduling may be achieved without the need for a running forecast of the future generation-demand balance. We examine the applicability of the above theory to future GB storage needs, and discuss how it may be used to enable the most economic dimensioning of such storage, with possible savings of tens of billions of pounds, relative to the use of a single technology.

Scheduling and dimensioning of heterogeneous energy stores, with applications to future GB storage needs

TL;DR

The paper tackles the scheduling and dimensioning of heterogeneous energy stores required for future net-zero electricity systems, where high renewable variability necessitates large-scale, multi-technology storage. It develops a value-function based framework that yields near-optimal real-time policies, reducing the per-step problem to a simple linear program under non-anticipatory assumptions. Theoretical results show that greedy policies suffice and that non-anticipatory strategies (e.g., GG DDF, GRTEF) perform well, with cross-charging enabling cooperation among stores. An applied GB case demonstrates substantial potential cost savings from a well-chosen mix of storage technologies, highlighting practical pathways for dimensioning long-term storage without foresight, and suggesting broader applicability to other regions.

Abstract

Future ``net-zero'' electricity systems in which all or most generation is renewable may require very high volumes of storage, provided jointly by a number of heterogeneous technologies, in order to manage the associated variability in the generation-demand balance. We consider the problems of scheduling and dimensioning such storage. We develop a value-function based approach to optimal scheduling, and show that, to a good approximation, the problem to be solved at each successive point in time reduces to a linear programme with a particularly simple solution. We show that approximately optimal scheduling may be achieved without the need for a running forecast of the future generation-demand balance. We examine the applicability of the above theory to future GB storage needs, and discuss how it may be used to enable the most economic dimensioning of such storage, with possible savings of tens of billions of pounds, relative to the use of a single technology.
Paper Structure (11 sections, 3 theorems, 12 equations, 8 figures, 5 tables)

This paper contains 11 sections, 3 theorems, 12 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Model
  3. Nature of optimal policies
  4. Greedy policies
  5. Non-anticipatory policies
  6. Value functions
  7. Application to GB energy storage needs
  8. Generation and demand data.
  9. Storage data and costs.
  10. Conclusions
  11. Proofs

Key Result

Proposition 1

Any feasible policy may be modified to be greedy while remaining feasible and while continuing to serve as least as much energy to each successive time $t$. Further, if the original policy is non-anticipatory, the modified policy may be taken to be non-anticipatory.

Figures (8)

  • Figure 1: Histogram and autocorrelation function of hourly residual energy (30% overcapacity).
  • Figure 2: Dependence of minimal store size on level of generation overcapacity for various (round-trip) efficiencies.
  • Figure 3: Example \ref{['ex:1']}: single long (hydrogen) store: cumulative unserved energy.
  • Figure 4: Example \ref{['ex:1']}: single long (hydrogen) store: successive store energy levels.
  • Figure 5: Example \ref{['ex:2']}: plot of cumulative unserved energy against time (black) together with lower bounding process (red).
  • ...and 3 more figures

Theorems & Definitions (9)

  • Proposition 1
  • Corollary 1
  • Proposition 2
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • proof : Proof of Proposition \ref{['proposition:greedy']}
  • proof : Proof of Proposition \ref{['proposition:lp']}